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Probabilistic Predictive Models for Silicon PV Cell Crack Stress and Power Loss

DuraMAT will establish comprehensive, physics-informed models and tools to quantify silicon photovoltaic (PV) cell crack spatial, mechanical, and electrical properties, and to predict future crack power loss.

We will combine in-situ measurement of internal cell stress, finite element modeling of modules/cells, image and electrical characterization techniques, dynamic mechanical loading, and automated image analysis and parameterization to build a predictive model for cell crack behavior in PV modules.

Initial power loss immediately following cell fracture is highly variable as it depends on the crack severity, location, and shape, among other characteristics. The associated power loss in the years of operation following the fracture event is even more difficult to forecast, as the evolution of cell crack properties is not well understood. The goal of this project is to develop a model chain to answer the following questions about PV cell cracks:

  • How does a crack change the electrical properties of a cell and what is the power loss?
  • How will the mechanical stress and electrical properties of these cracks evolve?
  • What will be the impact of these cracks on module power in the future?

To address the above questions in a predictive way, we consider cracks as existing physical, mechanical, and electrical features in the silicon PV cell. Crack formation in PV modules is a binary, probabilistic event that is difficult to predict in the real world due to the unpredictability of crack-inducing events. However, the evolution of crack-correlated mechanical and electrical properties under normal operating conditions are well-suited to predictive modeling.

Core Objective

Multi-Scale, Multi-Physics Modeling


Sandia National Laboratories, Arizona State University


The proposed work has several elements that will be useful both outside and within DuraMAT's planned comprehensive model chain. We will develop model and analysis components modularly and open source to ensure that they are immediately useful to the PV community. For example, busbar-compatible crack detection workflow and parameterization algorithms would be useful to industry members who have or plan to gather EL image data of their sites and would otherwise conduct qualitative or manual inspection of these large data sets. These tools would allow users to quantitatively assess the extent of cracking in their modules, with not just detection, but spatial and expected electrical properties.

Establishing probabilistic representations of cell cracks alongside predictive models for crack behavior also enables statistical (Monte Carlo) simulations of cracked modules. As a tool for industry, measured statistical distributions of crack parameters, together with the imposed stress and crack properties, could be input into our proposed finite element analysis model to predict crack behavior and future power loss. This approach could be used to valuate existing PV arrays or to de-risk or optimize new cell or module designs.


Image analysis software and reduced-order predictive degradation models developed in this project will be publicly available online via Github.


Hartley, J. Y., Owen-Bellini, M., Truman, T., Maes, A., Elce, E., Ward, A., Khraishi, T., & Roberts, S. A. (2020). Effects of Photovoltaic Module Materials and Design on Module Deformation Under Load. IEEE Journal of Photovoltaics, 10(3), 838–843.

Thermal-Mechanical-Electrical Model for PV Module-Level Failure Mechanisms

Bertoni, M., "Water and deflection dynamics under solar cell operating conditions," Photovoltaics Reliability Workshop, 23 Feb 2022.

Direct Imaging of Stress in Crystalline Silicon Modules

Karimi, A. M., Pierce, B. G., Fada, J. S., Parrilla, N. A., French, R. H., & Braid, J. L. (2020). PVimage: Package for PV Image Analysis and Machine Learning Modeling (v0.8.0) [Python3].

Karimi, A. M., Fada, J. S., Parrilla, N. A., Pierce, B. G., Koyuturk, M., French, R. H., & Braid, J. L. (2020). Generalized and Mechanistic PV Module Performance Prediction From Computer Vision and Machine Learning on Electroluminescence Images. IEEE Journal of Photovoltaics, 10(3), 878–887.

Whitaker, C. M., Pierce, B. G., Karimi, A. M., French, R. H., & Braid, J. L. (2020). PV Cell Cracks and Impacts on Electrical Performance. 2020 47th IEEE Photovoltaic Specialists Conference (PVSC), 1417–1422.

Effect of Cell Cracks on Module Power Loss and Degradation

GitHub: hackingmaterials/pv-vision

Fioresi, J. et al., "Automated Defect Detection and Localization in Photovoltaic Cells Using Semantic Segmentation of Electroluminescence Images," in IEEE Journal of Photovoltaics, vol. 12, no. 1, pp. 53-61, Jan. 2022.

Bosco, N., Springer, M., Liu, J., Venkat, S. N., & French, R. H. (2021). Employing Weibull Analysis and Weakest Link Theory to Resolve Crystalline Silicon PV Cell Strength Between Bare Cells and Reduced- and Full-Sized Modules. IEEE Journal of Photovoltaics, 1–11.

Kajari-Schröder, S., Kunze, I., & Köntges, M. (2012). Criticality of Cracks in PV Modules. Energy Procedia, 27(Supplement C), 658–663.

Buerhop, C., Wirsching, S., Bemm, A., Pickel, T., Hohmann, P., Nieß, M., Vodermayer, C., Huber, A., Glück, B., Mergheim, J., Camus, C., Hauch, J., & Brabec, C. J. (2018). Evolution of cell cracks in PV-modules under field and laboratory conditions. Progress in Photovoltaics: Research and Applications, 26(4), 261–272.

Silverman, T. J., Bliss, M., Abbas, A., Betts, T., Walls, M., & Repins, I. (2019). Movement of Cracked Silicon Solar Cells During Module Temperature Changes. 2019 IEEE 46th Photovoltaic Specialists Conference (PVSC), 1517–1520.

Silverman, T. J., Deceglie, M. G., Owen-Bellini, M. Hobbs, W. B., and Libby, C. "Cracked Solar Cell Performance Depends on Module Temperature," 2021 IEEE 48th Photovoltaic Specialists Conference (PVSC), 2021, pp. 1691-1692.


To learn more about this project, contact Jennifer Braid.

"Experiment" with images showing mini-module fabrication, x-ray topography, and in-situ EL +IV; "Analysis & Modeling" with charts showing crack parameterization and statistics, and finite element analysis and modeling heatmap images; "Initial Crack Distributions": Spatial Properties, Electrical Properties, and Internal Stress with an arrow pointing to "Proposed FEA Models": Crack Stress Evolution, Crack Electrical Devolution, and Cell Power Loss; "Current FEA Models": Module Stress, Imposed Stress with arrow pointing to "Proposed FEA Models"; Crack Evolution Model Chain Development: Define crack types and initial property statistical distributions, Characterize internal stress associated with crack types, Integrate existing FEA models for stress imposed on cell, Experimentally observe crack physical and electrical behavior, and Model and validate crack evolution behavior.